Fractional quantum couplers

Abstract

Fractional quantum coupler, a new type of quantum couplers that is composed of arrays of two coupled waveguides or a dual-core waveguide with intermodal coupling, within which the light waves diffraction is of the fractional-order differentiation, is put forward in the territory of fractional quantum mechanics. The modelling equations of such fractional couplers are derived in the framework of coupled nonlinear fractional Schrödinger equations with the space derivative of fractional order denoted by Lévy index α, and localized wave solutions as spatial optical solitons of these equations are constructed and their nonlinear propagation properties are discussed. Linear perturbation method based on linear stability analysis, and direct simulations are conducted to identify the stability and instability regions of the predicted solitons.